Abstract.
We prove that solutions of the homogeneous equation Lu=0, where L is a locally integrable vector field with smooth coefficients in two variables possess the F. and M. Riesz property. That is, if \(\Omega\) is an open subset of the plane with smooth boundary, \(u\in C^1(\Omega)\) satisfiesLu=0 on \(\Omega\), has tempered growth at the boundary, and its weak boundary value is a measure \(\mu\), then \(\mu\) is absolutely continuous with respect to Lebesgue measure on the noncharacteristic portion of \(\partial\Omega\).
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Received March 10, 2000 / Published online April 12, 2001
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Berhanu, S., Hounie, J. An F. and M. Riesz theorem for planar vector fields. Math Ann 320, 463–485 (2001). https://doi.org/10.1007/PL00004482
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DOI: https://doi.org/10.1007/PL00004482